Equalising and decoding device for frequency-selective channels

ABSTRACT

The invention relates to a channel equalizing and decoding device consisting of a series of modules, each of which comprises an equalizer ( 10 ) and a decoder with weighted output ( 20 ). The modules of rank higher than 1 receive (i) a sequence of samples coming from a sensor and delayed by a value equal to the processing time of preceding modules and (ii) the output from the preceding module. Said invention is characterized in that each of the modules comprises means for receiving at least two different sequences of samples and an equalizer that can determine one same equalized sequence of samples using the aforementioned minimum two sequences received as two different non-equalized representations of the sequence of samples to be determined.

The present patent application is a non-provisional application ofInternational Application No. PCT/FR02/00783, filed Mar. 5, 2002.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a channel equalization and decodingdevice for frequency selective channels.

2. Description of Related Art

In digital transmission, the solutions proposed generally use channelequalization and coding processes. In the conventional approach, theelementary channel equalization and coding functions are processedseparately, utilizing only part of the information placed at theirdisposal. Therefore, the overall performance of the receiver remainssuboptimal.

An aim of the invention is to remedy this drawback.

For a few years now, several authors prompted by the techniques ofturbo-codes [1] have proposed solutions based on a maximum likelihooddetector, an interference canceller and channel coding to combatinterference between symbols. Among these solutions let us brieflyrecall the most significant contributions.

In 1995, a receiver called a turbo-detector [2] associated a detectorbased on maximum a posteriori likelihood with a channel decoder, throughan iterative procedure. The performance obtained was then quasi-optimalfor many channels. However, the turbo-detector remained reserved ratherfor modulations with a small number of states and for channels havingshort impulse responses.

In 1997, another turbo-equalizer receiver [3] was devised with the aimof being able to reduce the complexity of the turbo-detector and ofbeing able to quasi-optimally equalize modulations with a large numberof states on channels exhibiting considerable spreading with respect tothe symbol duration.

An aim of the invention is to improve the performance of both of theaforementioned receivers.

BRIEF SUMMARY OF THE INVENTION

To do this, a device according to the invention is a channelequalization and decoding device comprising a series of modules whicheach comprise an equalizer and a decoder with weighted outputs, andwhose modules of rank greater than 1 receive, on the one hand, a stringof samples emanating from a sensor and delayed by a quantity equal tothe processing time of the previous modules, and, on the other hand, theoutput of the previous module, characterized in that the modules eachcomprise means of reception of at least two strings of different samplesand an equalizer able to determine one and the same equalized string ofsamples by utilizing these at least two strings received as twounequalized different representations of the string of samples to bedetermined.

The invention uses the spatial and/or temporal diversity provided by anantenna possessing several sensors (multi-channel receivers) from whichsensors there typically emanate respectively the two strings of samplesforming the two different representations. The invention differs fromthe contributions [4-8] through its multi-channel processing of theinformation received and/or the possibility of using modulations with alarge number of states for transmissions with considerable temporalspreading.

In this way, spatial and/or temporal diversity of reception whichmarkedly improves the results obtained is utilized.

A multi-channel signal is equalized and one and the same block ofreceived data is decoded repeatedly using the information provided bythe previous processing.

BRIEF DESCRIPTION OF THE DRAWINGS

Other characteristics, aims and advantages of the invention will becomeapparent on reading the detailed description which follows, given withreference to the appended figures in which:

FIG. 1 a represents a transmission chain of bit-interleaver type;

FIG. 1 b represents a transmission chain of symbol-interleaver type;

FIG. 2 diagrammatically illustrates an iterative structure of amulti-channel equalization and channel decoding device in accordancewith a possible embodiment of the invention;

FIG. 3 diagrammatically represents a possible structure of a receivermodule according to the invention;

FIG. 4 a diagrammatically represents a possible decomposition of achannel decoder with M-ary weighted output and input, used in anembodiment of the invention, in particular in respect of transmissionswith multistate modulations in the case of a bit-interleaver;

FIG. 4 b diagrammatically represents a possible decomposition of achannel decoder with M-ary weighted output and input, used in anembodiment of the invention, in particular in respect of transmissionswith multistate modulations in the case of a symbol-interleaver;

FIG. 5 diagrammatically represents an embodiment of a multi-channelequalizer according to the invention;

FIG. 6 diagrammatically represents another possibility for theembodiment of a multi-channel equalizer according to the invention;

FIG. 7 is a graph which gives the binary error rate after channeldecoding as a function of a ratio Eb/N0 and which illustratesperformance of a device of the type of that represented in FIGS. 2, 3,and 5 for an PM2 modulation on a multi-channel pathway;

FIG. 8 is a graph which gives the binary error rate after channeldecoding as a function of the ratio Eb/N0 and which illustratesperformance of a device of the type of that represented in FIGS. 2, 3,and 6 for an PM2 modulation on a multi-channel pathway.

DETAILED DESCRIPTION OF THE INVENTION

Illustrated in FIGS. 1 a and 1 b is the principle of a data transmissionchain. A channel coder 1 is fed with mutually independent binary dataα_(k) uniformly distributed over the set {0; 1}, at a rate of one dataitem every T_(b) seconds. The data leaving the channel coder 1 aretransposed onto the set {−1; 1} and denoted c_(k).

Each passage of a set of 2m coded data C_(k) through the interleaverreferenced 2 and through the binary to symbol converter (BSC) referenced3 generates a complex symbol d_(n)=a_(n)+jb_(n) of variance σ² _(d). Thesymbols a_(n) and b_(n) take their values in the alphabet {±1 . . . ,±(2p+1), . . . , ±(√M−1)} with √M=2^(m). This operation can, withoutloss of generality, integrate the techniques of trellis-codedmodulation, of differential coding or any other system making itpossible to associate a modulation symbol with a set of binary elements.The transmission chains depicted in FIGS. 1 a and 1 b differ regardingthe location of an interleaver 2 which can be placed respectivelyupstream (bit interleaver) or downstream (symbol interleaver) of the BSCreferenced 3. The modulation symbols, denoted dn, are then presented tothe input of a modulator on two quadrature carriers.

The assembly consisting of modulator, transmission medium, demodulators,and transmit and receive filters is modeled by a multi-channelequivalent discrete pathway 4, where each channel i, i=1, . . . , N, isdisturbed by centered, Gaussian additive noise w_(i,n) of variance σ_(i)². The output of each channel is equal to:

$\begin{matrix}{r_{i,n} = {{\sum\limits_{l = 0}^{Li}{h_{i,l}d_{n - 1}}} + w_{i,n}}} & (1)\end{matrix}$where the h_(i,1) are the coefficients of the pathway corresponding tochannel i and such that the transfer function associated with thischannel may be written:

$\begin{matrix}{{H_{i}(z)} = {\sum\limits_{l = 0}^{L_{i}}{h_{i,l}z^{- 1}}}} & (2)\end{matrix}$

The coefficients of the pathways of the various channels are assumed tobe normalized in such a way that the signal received at the level of thereceiver, here denoted 5, is of unit power:

$\begin{matrix}{{\sum\limits_{i = 1}^{N}\rho_{i}} = {{1\mspace{14mu}{with}\mspace{14mu}\rho_{i}} = {\sum\limits_{l = 0}^{L_{i}}{h_{i,l}}^{2}}}} & (3)\end{matrix}$

Considering the noise w_(i,n) to be mutually uncorrelated, the varianceof the noise seen by a receiver referenced 5 is equal to:

$\begin{matrix}{\sigma_{noise}^{2} = {\sum\limits_{i = 1}^{N}\sigma_{i}^{2}}} & (4)\end{matrix}$

The signal-to-noise ratio (SNR) at the input of the turbo-equalizer isequal to:

$\begin{matrix}{{SNR} = {\frac{\sigma_{d}^{2}}{\sigma_{noise}^{2}} = {R\frac{E_{b}}{N_{0}}{\log_{2}(M)}}}} & (5)\end{matrix}$where E_(b) is the mean energy received per data item transmitted, N₀the spectral power density of the noise at the input of the receiver 5and R the rate of the channel coder 1.

In what follows, an elementary processing of an information block willbe referred to as a module. As represented in FIG. 3, each module p(p=1,. . . , P) comprises a multi-channel equalizer 10 (in particular anequalizer able to utilize the signals picked up simultaneously byseveral sensors in parallel), and a channel decoder 20 integrating theinterleaving and deinterleaving functions. The multi-channel equalizer10 of the modules of rank greater than 1 must be able to utilize theestimated data provided by the channel decoder of the lower-rankmodules.

In the case of multistate modulations, the channel decoder 20 can besplit into five distinct elements (FIGS. 4 a and 4 b), i.e. a symbol tobinary converter (SBC) 22, a deinterleaver 23, a channel decoder withbinary weighted input and output 24, an interleaver 25 and a binary tosymbol converter (BSC) 26. The site of the interleaver is locateddownstream or upstream of the SBC 22 and reciprocally for the BSC 26 inaccordance with the transmit diagram.

In what follows, we shall present two embodiments. One, called amulti-channel turbo-equalizer (MCTE), is composed of simple digitalfilters and the other, called a multi-channel turbo-detector (MCTD),associates digital filters and a maximum a posteriori likelihooddetector with multiple inputs.

The structure of the multi-channel equalizer according to the firstvariant (MCTE), represented in FIG. 5, comprises a bank of filters 11comprising as many filters as there are reception channels. An adder 12then sums the set of outputs from the bank of filters 11. The outputfrom a filter Q, referenced 13, fed either with the decided data of theiteration in progress, or with the estimated data obtained from theprevious module, is then subtracted from this signal.

For the module of rank 1, the transverse filter Q is fed either with theoutput from the equalizer of this same module, or with decided data atthe output of the equalizer of this same module. The transverse filter Qis fed with the output from the previous module, and advantageouslyeither with the output from the equalizer of this same module, or withdecided data at the output of the equalizer of this same module for themodule of rank 1.

This last filter 13 makes it possible to reconstruct some or all of theinter-symbol interference present at the output of the adder 12 in amanner similar to the teaching of FR 2 763 454.

To describe the device, we have considered an PM2 modulation and a fixednumber N=2 of channels. The transmission pathways are such that thepowers of the signal and of the noise are identical on each channel. Forthe first module (p=1), the linear equalizer optimal in the mean squareerror sense can then be embodied, apart from by the filter Q, by twotransverse filters with transfer function P_(i)(Z) and a summator.

$\begin{matrix}{{{P_{i}(z)} = {{\frac{{H_{i}^{*}\left( {1/z^{*}} \right)}\sigma_{d}^{2}}{{\left( {{{H_{1}(z)}{H_{1}^{*}\left( {1/z^{*}} \right)}} + {{H_{2}(z)}{H_{2}^{*}\left( {1/z^{*}} \right)}}} \right)\sigma_{d}^{2}} + \sigma_{noise}^{2}}i} = 1}},{2;{p = 1}}} & (6)\end{matrix}$with H₁=h_(1,1); h_(1,2); . . . h_(1,L1) and H₂=h_(2,1); h_(2,2); . . .; h_(2,L2).

These filters are generally embodied in transverse form, but may equallywell be embodied by cascading a transverse filter and a recursivefilter. It is also entirely possible to use a simple matched filter orelse a decision feedback nonlinear equalizer.

The output of the multi-channel equalizer 10 feeds the input of thechannel decoder 20 with weighted inputs and outputs. The output from thechannel decoder 20 provides the estimated data that will be used by thenext module to feed a filter Q(z) referenced 13. The iterative procedureis then instigated and can continue. When the number of iterations issufficient and the MCTE has operated correctly, then the transferfunctions of the filters P_(i)(z) and Q(z) are close or equal to:P _(i)(z)=H* _(i)(1/z*) i=1,2; p>1  (7)

The number of coefficients of these filters is finite. These filters areQ(z)=H ₁ H* ₁(1/z*)+H ₂(z)H* ₂(1/z*)−1 p>1  (8)embodied in transverse form.

The manner in which the coefficients of the filters P₁, P₂ and Q of theequalizers are determined in practice as well as the manner in which theweighted outputs of the channel decoder 20 are obtained can be those setforth in FR 2 763 454.

To illustrate the manner of operation of the MCTE, we have consideredtwo highly frequency-selective channels whose non-normalized discreteimpulse responses are equal to:H₁=[0.38 0.6 0.6 0.38]H ₂=[0.8264−0.1653 0.8512 0.1636 0.81]

The coefficients of the filters are calculated from relations (6), (7),and (8), assuming that the coefficients of H₁ and H₂ are known. For thesimulations, the transmission chain depicted in FIG. 1 b has beenconsidered together with an interleaving of size 256×256 and thetransmitting of more than 1 million binary elements. Channel coding iscarried out by a rate ½ convolutional coder with octal generatingpolynomials (23, 35).

The performance of the MCTE is represented in FIG. 7. The dashed curverepresents the performance obtained on the frequency unselectiveGaussian channel with coding and the solid curves the performanceobtained at the output of the MCTE for various iterations.

These results show that the MCTE is very efficient in combatinginter-symbol interference and rivals the performance of the frequencyunselective Gaussian channel when the signal-to-noise ratio exceeds afew dB.

A second embodiment, which is a receiver based on the use of amulti-channel detector, will now be described.

The structure of the multi-channel detector of the MCTE, represented inFIG. 6, comprises a bank of filters 14 comprising as many filters asthere are reception channels. The outputs from the bank of filters 14 aswell as the estimated data of a previous module feed the input of amulti-channel MAP detector 15 based on maximum a posteriori likelihood(detector with weighted outputs).

The weighted output of the detector 15 is deduced from a likelihoodratio logarithm calculation. An intrinsic value can be obtained bysubtracting the previous module's estimated data, weighted by acoefficient, from the output of the detector 15.

It should be pointed out that, for the module of rank 1, the estimateddata provided by the previous module are not known. They will be takenequal to zero, their reliability being considered to be nil.

To describe this device, we have considered an PM2 modulation and afixed number N=2 of channels. The transmission pathways are such thatthe powers of the signal and of the noise are identical on each channel.We have also assumed that the filters 14 preceding the detector 15possessed just a single coefficient equal to 1. In this case, detectingthe most likely sequence then amounts to minimizing the metric (9) belowwith respect to all the possible sequences j:

$\begin{matrix}{{\min\limits_{j}\mspace{11mu}{M_{n}(j)}} = {{\sum\limits_{k = 0}^{n}{{r_{l,k} - {\sum\limits_{l = 0}^{L_{i}}{h_{1,l}d_{k - l}^{(j)}}}}}^{2}} + {{r_{2,k} - {\sum\limits_{l = 0}^{L_{i}}{h_{2,l}d_{k - l}^{(j)}}}}}^{2} + {\gamma{{{\overset{\sim}{d}}_{k} - d_{k}^{(j)}}}^{2}}}} & (9)\end{matrix}$where γ is a positive coefficient and dk the estimated data itemobtained from the output of the channel decoder of a previous module,and which is easily calculated on the model of the process set forth inFR 2 730 370.

The output from the detector 15 provides a likelihood ratio logarithmfrom which is subtracted the estimated data item d_(k) multiplied by thecoefficient γ as in FR 2 730 370. The extrinsic value obtained feeds theinput of the channel decoder 20 with weighted input and output (FIG. 3).The output of the channel decoder 20 provides the estimated data thatwill be used by the next module to improve the performance of itsdetector 15. It will be noted that, for the first iteration (p=1), theestimated data are not known and are regarded as zero values.

The manner in which the coefficients of the filters H₁(z) and H₂(z) aredetermined in practice and the manner in which the weighted outputs ofthe detector and of the channel decoder are obtained are in themselveswell known. Reference may be made in particular to FR 2 730 370.

To illustrate the manner of operation of the MCTD, we have consideredthe two channels H₁ and H₂ described previously.

The coefficients of H1 and H2 are assumed to be known to the receiver.For the simulations, the transmission chain depicted in FIG. 1 b hasbeen considered together with an interleaving of size 256×256 and thetransmitting of more than 1 million binary elements. Channel coding iscarried out by a rate ½ convolutional coder with octal generatingpolynomials (23, 35).

The performance of the MCTD is represented in FIG. 8. The dashed curverepresents the performance obtained on the frequency unselectiveGaussian channel with coding and the solid curves the performanceobtained at the output of the MCTD for various iterations.

These results show that the MCTD is very efficient in combatinginter-symbol interference and rivals the performance of the frequencyunselective Gaussian channel when the signal-to-noise ratio exceeds afew dB.

The devices just described advantageously find application in anymulti-channel receiver for a system for digital communication onfrequency-selective channels possessing (convolutional or block) channelcoding and interleaving.

Two distinct structures have been proposed. The first structure (MCTE)makes it possible to equalize transmission pathways possessing longimpulse responses for transmissions by modulations with a large numberof states. The second structure (MCTD) is better suited to modulationswith a small number of states for transmission pathways with smalltemporal dispersion.

The invention is applicable to any transmission system using linearmodulations such as phase modulations (PM), amplitude modulations onquadrature carriers (QAM), modulations associated with a differentialcoding, trellis-coded modulations (TCM) and nonlinear modulations thatcan be decomposed into sums of linear modulations (GMSK, CPM, . . . ).

REFERENCES

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1. A channel equalization and decoding device in a context ofmulti-channel reception comprising: a series of modules each including adecoder (20) with weighted outputs, a module of rank p=1 receives astring of samples emanating from a sensor and each module of rank pgreater than 1 receives, on the one hand, said string of samplesemanating from the sensor and delayed by a quantity equal to theprocessing time of the previous modules of rank 1 to p−1, and, on theother hand, the output of the previous module of rank 1 to p−1, whereinthe module of rank 1 further receives at least one other stringemanating from another sensor and the modules of rank p greater than 1receive said at least one other string of samples emanating from theother sensor and delayed by a quantity equal to the processing time ofthe modules of rank 1 to p−1, the at least two strings of samples beingdifferent and a multi-channel equalizer to determine one and the sameequalized string of samples by utilizing the at least two stringsreceived as two unequalized different representations of a string ofsamples to be determined.
 2. The device as claimed in claim 1, whereinthe equalizer of each module comprises means for implementing twodifferent equalization processings on respectively the at least twostrings received.
 3. The device as claimed in claim 1 or claim 2,wherein each module of the series of modules comprises: the equalizerincluding a detector with weighted outputs and inputs (15) and a bank offilters (14) placed so as to each be fed with a string of samples fromamong said at least two strings of samples received, the detector (15)receiving, on the one hand, the outputs from the filters (14) and, onthe other hand, at least one output from the previous module in respectof the modules of rank greater than
 1. 4. The device as claimed in claim1, wherein the decoder (20) is a channel decoder with M-ary weightedoutputs and inputs including five functions that are either a symbol tobinary converter SBC (22), a deinterleaving function (23), a decodingfunction with binary weighted outputs and inputs (24), an interleaver(25) and a binary to symbol converter BSC (26).
 5. The device as claimedin claim 4, wherein each module comprises a deinterleaver (23) betweenthe SBC (22) and the decoder (24), and an interleaver (25) between thedecoder (24) and the BSC (26).
 6. The device as claimed in claim 4,wherein each module comprises a symbol to binary converter (22) betweenthe deinterleaver (23) and the decoder (24) and a binary to symbolconverter BSC (26) between the decoder (24) and the interleaver (25). 7.The device as claimed in claim 4, wherein the SBC (22) integrates atrellis-coded modulation.
 8. A channel equalization and decoding devicecomprising: a series of modules each including a decoder with weightedoutputs, a module of rank p=1 receives a string of samples emanatingfrom a sensor and whose modules of rank p greater than 1 receive, on theone hand, the string of samples emanating from the sensor and delayed bya quantity equal to the processing time of the previous modules, and, onthe other hand, the output of the previous module wherein the module ofrank 1 further receives at least one other string emanating from anothersensor and the modules of rank p greater than 1 receive said at leastone other string of samples emanating from the other sensor and delayedby a quantity equal to the processing time of the modules of rank 1 top−1, the at least two strings of samples being different and anequalizer to determine one and the same equalized string of samples byutilizing the at least two strings received as two unequalized differentrepresentations of the string of samples to be determined, the equalizer(10) of each module comprises: a bank (11) of at least two transversefilters fed respectively with said at least two sample strings received,an adder (12) placed downstream of the filter bank (11), anothertransverse filter (13) fed by an output of the previous module, andmeans for subtracting a sample string obtained from the output of theadder to a sample string obtained from the output of the othertransverse filter.
 9. The device as claimed in claim 8, wherein thesample string outputted from said other transverse filter (13)represents at least partially the interference present at the output ofthe adder.
 10. The device as claimed in claim 8, wherein the module ofrank 1 comprises means for feeding its said other transverse filter (13)with data tapped off or decided at the output of the equalizer (10) ofthis same module.